In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides. We assume that at least one of is Hamiltonian. Under assumption, no more than cycle. This characterizes integrals.

The generalized quantum double lattice realization of 2d topological orders based on Hopf algebras is discussed in this work. Both left-module and right-module constructions are investigated. ribbon operators the classification excitations representations discussed. To generalize model to a surface with boundaries defects, we present systematic construction boundary Hamiltonian domain wall Hami...

Foreword These notes cover a short course on symplectic toric manifolds, delivered in six lectures at the summer school on Symplectic Geometry of Integrable Hamiltonian Systems, mostly for graduate students, held at the Centre de Recerca Matemàtica in Barcelona in July of 2001. The goal of this course is to provide a fast elementary introduction to toric manifolds (i.e., smooth toric varieties)...

Exact numerical diagonalization of the Bohr Hamiltonian by SU(1, 1) × SO(5) methods is used to obtain detailed quantitative predictions for single-phonon and multi-phonon excitations in well-deformed rotor nuclei. Dynamical γ deformation is found to significantly influence the predictions through its coupling to the rotational motion. Basic signatures for the onset of rigid triaxial deformation...

We construct XX-and Hubbard-like models based on unitary superalgebras gl(N |M) generalising Shastry's and Maassarani's approach of the algebraic case. We introduce the R-matrix of the gl(N |M) XX model and that of the Hubbard model defined by coupling two independent XX models. In both cases, we show that the R-matrices satisfy the Yang–Baxter equation, we derive the corresponding local Hamilt...